with \(f\equiv pp\rightarrow HH@LHC14\)  and \(e^{-}e^{+}\rightarrow ZHH@ILC500\) .
For the process \(f\equiv pp\rightarrow HH@LHC14\) , we have \(\sigma _{G}\equiv \sigma _{}=70.1\,\mathrm {fb}\) , \(\sigma _{\lambda }\equiv \sigma _{\triangle }=9.66\,\mathrm {fb}\) 
and \(\sigma _{G\lambda }\equiv \sigma _{\triangle }=-49.9\,\mathrm {fb}\) 
are the box, triangle and interference contributions to the total
cross section, respectively [1]}. Using MadGraph [2]},
we find \(\sigma _{G}=0.0837~\mathrm {fb},~\sigma _{\lambda }=0.01565~\mathrm {fb}\)  and \(\sigma _{G\lambda }=0.05685~\mathrm {fb}\) 
for the process \(e^{-}e^{+}\rightarrow ZHH@ILC500\) . The coefficients
\(\xi _{i}\)  are given at the CM energy \(\sqrt{s}\)  by [3]}
\(\xi _{1}=c_{\alpha }^{4},\,\xi _{2} & =\left|\mathcal {P}\right|^{2},\,\xi _{3}=c_{\alpha }^{2}\Re \left(\mathcal {P}\right),\,\mathcal {P}=c_{\alpha }\frac{\lambda _{HHH}}{\lambda _{hhh}^{SM}}+s_{\alpha }\frac{\lambda _{HHS}}{\lambda _{hhh}^{SM}}\frac{s-m_{h}^{2}+im_{h}\Gamma _{h}}{s-m_{S}^{2}+im_{S}\Gamma _{S}}\) 
